Statistically Robust Transceiver Design for Broadcast Channels with Uncertainty

We consider the design of linear transceivers for the downlink of a multiuser communication system in the presence of uncertain channel state information (CSI) at the base station. We focus on systems in which the base station has multiple antennas and each user has a single antenna, and we consider a stochastic model for the uncertainty in the CSI. We study the joint design of a linear precoding matrix at the base station and the equalizing gains at the receivers so as to minimize the average, over channel uncertainty, of the total mean-square-error (MSE). By generalizing the MSE duality between the broadcast channel (BC) and multiple access channel (MAC) to scenarios with uncertain CSI, we obtain a relation between the desired robust broadcast transceivers and the corresponding transceivers that optimize the same performance metric for the dual multiple access channel. Furthermore, we present a convex optimization formulation for the robust transceivers of the dual MAC that can be efficiently solved. Our simulations indicate that the proposed approach can significantly reduce the sensitivity of the downlink to uncertainty in the CSI, and can provide improved performance over that of existing robust designs.